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MeganDarling
A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use? 3 lbs peanuts, 6 lbs almonds, 2 lbs raisins 8 lbs peanuts, 1 lb almonds, 2 lbs raisins 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins 8 lbs peanuts, 2 lbs almonds, 1 lbs raisins
Start off by defining variables
let x = amount of peanuts (in pounds), y = amount of almonds (in pounds) and z = amount of raisins (in pounds)
If "A food store makes a 11–pound mixture of peanuts, almonds, and raisins" then what does this mean?
That they add up to 11 pounds haha
good, so x y and z add to 11, which means x+y+z = 11
that's one equation
But then we have to factor in how much they cost..
We also know that "The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound" So x lbs of peanuts cost 1.5x dollars, y lbs of almonds cost 3y dollars, and z lbs of raisins cost 1.5z dollars They total 1.5x + 3y + 1.5z dollars
this total cost is given to be $21 so 1.5x + 3y + 1.5z = 21
so like, 1.50x+3.00y+1.50=21..
Haha Okey you already said that x.x my bad
1.50z* I meant btw haha. I get that indeed.
close, you mean to say 1.50x+3.00y+1.50z=21 but you got it
And don't forget twice the peanuts!
that's your 2nd equation
twice the peanuts as what?
it says, the recipe calls for twice as many peanuts as almonds O.o
good, so the equation for that is?
ermm.. I dunno lol.. x(times2y)+y+z=11 O.O I have no idea.
knew it was wrong x.x
Amount of peanuts = 2 times (amount of almonds)
y = 2 times x or just y = 2x
oh pshh I should have thought of that x.x
so you have these 3 equations x+y+z = 11 1.5x + 3y + 1.5z = 21 y = 2x
you can use them to solve for x, y and z
I'll get you started
Lol I can't because I'm stupid, But smart people definitely can haha
x+y+z = 11 x+2x+z = 11 3x+z = 11 --------------------- 1.5x + 3y + 1.5z = 21 1.5x + 3(2x) + 1.5z = 21 1.5x + 6x + 1.5z = 21 7.5x + 1.5z = 21
so after plugging in y = 2x, you now have the new system 3x+z = 11 7.5x + 1.5z = 21
O.o That all made absolutely no sense to me but it seems to for you and that's good enough for me
where are you lost?
I took x+y+z = 11 plugged in y = 2x (ie replaced every 'y' with '2x') to get x+2x+z = 11 then I combined like terms to get 3x+z = 11
I did the same with 1.5x + 3y + 1.5z = 21 to get 7.5x + 1.5z = 21
oh okay ! I see now, sorry it's really late and I'm super tired :/
so you have 3x+z = 11 7.5x + 1.5z = 21 now
solve the first equation for z to get this 3x+z = 11 3x+z - 3x = 11 - 3x z = 11 - 3x
Since z = 11 - 3x, you can plug it into the other equation and solve for x 7.5x + 1.5z = 21 7.5x + 1.5(11 - 3x) = 21 Solve for x
oh wait, i made a variable mistake...i switched x and y one sec
Let me fix real quick
I was thinking that haha x) ..
uhh ? your comment disappeared .. :o
it should be x = 2y, not y = 2x so x+y+z = 11 2y+y+z = 11 3y + z = 11 z = 11 - 3y --------------------------- 1.5x + 3y + 1.5z = 21 1.5(2y) + 3y + 1.5z = 21 3y + 3y + 1.5z = 21 6y + 1.5z = 21 =========================== 6y + 1.5z = 21 6y + 1.5(11 - 3y) = 21 Solve that last equation for y
Solve 6y + 1.5(11 - 3y) = 21 for y
Aw man I have to go to bed soon I'm dead tired x.x
What do you get when you solve that equation for y
ergh I dunno x.x I'm brain dead
Then give it a break, get some sleep and you'll tackle it in the morning
Oh no I keep losing connection >.<